Quantum phase transition in a one-dimensional Holstein-Hubbard model at half-filling in the thermodynamic limit: A quantum entanglement approach

Sankar, I. V.; Chatterjee, Ashok

doi:10.1016/j.physb.2016.02.027

Cited by 12 publications

(5 citation statements)

References 31 publications

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“…Subsequently, several other studies have also shown the evidence of this metallic phase 16 – 27 . This problem has recently been studied by Sankar and Chatterjee 28 by calculating the von Neuman entropy which gives a measure of the Quantum Entanglement (QE) and hence the metallicity and the quantum nature of the phase transition associated with the SDW-CDW transition. The existence of the reasonable evidence of the intermediate metallic phase at the SDW-CDW cross-over region notwithstanding, this issue is not conclusively settled because the calculation of TC 13 has been restricted to a very simple phonon state and the calculation of KC 14 is only marginally better.…”

Section: Introductionmentioning

confidence: 99%

Metallicity in a Holstein-Hubbard Chain at Half Filling with Gaussian Anharmonicity

Lavanya

Sankar

Chatterjee

2017

Sci Rep

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The Holstein-Hubbard model with Gaussian phonon anharmonicity is studied in one-dimension at half filling using a variational method based on a series of canonical transformations. A fairly accurate phonon state is chosen to average the transformed Holstein-Hubbard Hamiltonian to obtain an effective Hubbard model which is then solved using the exact Bethe - ansatz following Lieb and Wu to obtain the ground state energy, the average lattice displacement and the renormalized parameters. The Mott-Hubbard criterion, local spin moment and the von Neumann entropy (which is a measure of quantum entanglement) are calculated to determine the ground state phase diagram which shows that the width of the metallic phase flanked by the SDW and CDW phases increases with increasing anharmonicity at low and moderate values of anharmonicity but eventually saturates when the anharmonicity becomes substantially large.

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Section: Introductionmentioning

confidence: 99%

Metallicity in a Holstein-Hubbard Chain at Half Filling with Gaussian Anharmonicity

Lavanya

Sankar

Chatterjee

2017

Sci Rep

Self Cite

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“…To tackle the Hubbard-Holstein model, early attempts have extended it to a variational transformation 17,18 . These transformations have shown advantages in solving the Holstein model 36 , Hubbard-Holstein model 37,38 , Anderson-Holstein model 39,40 , and anharmonic phonons 41 . However, due to the limitation of the numerical treatment on either the phonon or electronic side, these variational transformations were restricted only to a q−independent λ q .…”

Section: Model and Derivationsmentioning

confidence: 99%

Zero-Temperature Phases of the 2D Hubbard-Holstein Model: A Non-Gaussian Exact Diagonalization Study

Wang,

Esterlis,

Shi

et al. 2019

Preprint

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We propose a novel numerical method which embeds the variational non-Gaussian wavefunction approach with exact diagonalization, allowing for efficient treatment of correlated systems with both electron-electron and electron-phonon interactions. Using a generalized polaron transformation, we construct a variational wavefunction that absorbs entanglement between electrons and phonons into a variational non-Gaussian transformation; exact diagonalization is then used to treat the electronic part of the wavefunction exactly, thus taking into account high-order correlation effects beyond the Gaussian level. Keeping the full electronic Hilbert space, the complexity is increased only by a polynomial scaling factor relative to the exact diagonalization calculation for pure electrons.As an example, we use this method to study ground-state properties of the two-dimensional Hubbard-Holstein model, providing evidence for the existence of intervening phases between the spin and charge-ordered states. In particular, we find one of the intervening phases has strong charge susceptibility and binding energy, but is distinct from a CDW-ordered state; while the other intervening phase displays superconductivity at weak couplings. This method, as a general framework, can be extended to treat excited states and dynamics, as well as a wide range of systems with both electron-electron and electron-boson interactions.

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“…Для исследования влияния электрон-фононного взаимодействия удобна модель Холстейна−Хаббарда (ННМ), где учитывается и электрон-электронное (как правило, только одноцентровое) отталкивание [11][12][13][14][15][16][17][18][19][20]. ННМ применяется к описанию сверхпроводимости (в том числе, высокотемпературной), ВСП и ВЗП, поляронов и биполяронов в 3D-, 2D-и 1D-решетках, а также кластерах.…”

Section: Introductionunclassified

Электрон-Электронное И Электрон-Фононное Взаимодействия В Графене На Полупроводниковой Подложке: Простые Оценки

Давыдов¹

2018

Физика И Техника Полупроводников

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The problem of epitaxial graphene formed on a semiconductor substrate is considered in the context of the extended Hubbard and Holstein–Hubbard models for electron–electron and electron–phonon interactions. The Haldane–Anderson model is chosen for the density of states of the substrate. Three regions of the phase diagram, specifically, spin- and charge-density waves and a spin- and charge-homogeneous paramagnetic state are considered. For a number of special cases used as examples, the similarities and differences of the electron states of graphene on semiconductor and metal substrates are demonstrated. It is shown that the main difference arises, if the Dirac point of graphene lies within the band gap of the semiconductor. Numerical estimations are performed for a SiC substrate.

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Quantum phase transition in a one-dimensional Holstein-Hubbard model at half-filling in the thermodynamic limit: A quantum entanglement approach

Cited by 12 publications

References 31 publications

Metallicity in a Holstein-Hubbard Chain at Half Filling with Gaussian Anharmonicity

Metallicity in a Holstein-Hubbard Chain at Half Filling with Gaussian Anharmonicity

Zero-Temperature Phases of the 2D Hubbard-Holstein Model: A Non-Gaussian Exact Diagonalization Study

Электрон-Электронное И Электрон-Фононное Взаимодействия В Графене На Полупроводниковой Подложке: Простые Оценки

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